Atiyah–Bott fixed-point theorem: Difference between revisions

Revision as of 21:34, 28 June 2019

Revision as of 21:39, 28 June 2019

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:<math>\varphi_j \colon f^{-1}(E_j) \to E_j</math>

for each ''j'', such that the resulting maps on [[section (fiber bundle)|sections]] give rise to an [[endomorphism]] of an [[elliptic complex]] <math>T</math>. Such an endomorphism <math>T</math> has ''Lefschetz number''

:<math>L(T),</math>

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==References==

*M.{{Citation|first1=Michael F.|last1= Atiyah;|author1-link=Michael R.Atiyah| first2= Raoul|last2= Bott ''| author2-link=Raoul Bott|title=A Lefschetz Fixed Point Formula for Elliptic Differential Operators.''|journal= Bull.[[Bulletin Am.of Math.the Soc.American Mathematical Society]] |volume=72 (|year=1966),|pages= 245–50. This states a theorem calculating the Lefschetz number of an endomorphism of an elliptic complex.

|url=http://www.ams.org/bull/1966-72-02/S0002-9904-1966-11483-0/home.html| doi=10.1090/S0002-9904-1966-11483-0|issue=2 }}. This states a theorem calculating the Lefschetz number of an endomorphism of an elliptic complex.

*M. F. Atiyah; R. Bott ''A Lefschetz Fixed Point Formula for Elliptic Complexes:'' [https://www.jstor.org/stable/1970694 ''A Lefschetz Fixed Point Formula for Elliptic Complexes: I''] [https://www.jstor.org/stable/1970721 ''II. Applications''] The [[Annals of Mathematics]] 2nd Ser., Vol. 86, No. 2 (Sep., 1967), pp.&nbsp;374–407 and Vol. 88, No. 3 (Nov., 1968), pp.&nbsp;451–491. These gives the proofs and some applications of the results announced in the previous paper.